Perhaps it should come as no surprise that the day after Tory councillors have been publicly criticising their own party's education plans, a number of headteachers – many of them running selective schools – should publish a letter in the Daily Telegraph defending the very same plans. The letter feels like it has the fingerprints of Conservative HQ all over it.

First, let's not forget the fact that some eminent people on the Conservatives' own side are very dubious about their plans for schools. Yesterday, Paul Carter, a senior Tory councillor, appeared to question the party's "free schools" scheme. Carter, the Kent county council leader, said: "The more academies and free schools you operate, under the current academy funding arrangements, the less maintained schools would get." Although Carter later stated his full backing for the Tories' schemes, it's worth considering his candid analysis before he was "leaned on".

As an expert with a strategic overview of a county, he knows that the Conservatives' plans to introduce a "free market" into the school system could cause very severe problems with popular schools being vastly over-subscribed and less popular ones being left to rot. This is already happening to a certain extent, but the Conservatives' plans will mean that the drift in this direction will see popular schools splitting at the seams while the unpopular ones starve to death. But, even more importantly, as Carter hinted at, the Tories' plans will greatly increase the inequalities in our society, with the schools that have opted out of local authority control being more favourably funded than their maintained counterparts.

It was in the context of this devastating critique that the letter to the Telegraph was sent. In the missive, 31 heads and governors specifically endorsed the Conservative's plans to give high-performing state schools self-rule within months of a general election victory. These schools will be allowed to convert into semi-independent academies as early as September this year if the Tories win, giving them more power over the curriculum, qualifications, staff, budgets and, most crucially, admissions. Perhaps it should come as no surprise that a number of the headteachers supporting the Tories' plans run grammar schools – schools desperate to maintain their ability to select their own pupils.

But as research by the Campaign for State Education (Case) shows, grammar schools have the highest levels of social segregation with barely 3% of pupils attending them coming from socially disadvantaged backgrounds. Moreover, GCSE league tables consistently show that the lowest-attaining schools in the country are in areas where a grammar school system persists.

All the signatories of the letter are part of the Foundation, AidedSchools and Academies National Association (Fasna) – a national forum for primary, secondary and special self-governing schools, which means academies and schools that are aided, foundation or trust. Again, Case research shows that these schools already admit children from wealthier backgrounds than their local authority counterparts. If the Tory's plans are implemented, these schools will have even greater control over their admissions policies, and will no doubt admit even less poor children than they already do. As a teacher and a parent, I've increasingly come to recognise the importance of all schools taking their fair share of pupils from challenging and disadvantaged backgrounds: it's important for all children to mix with everyone in their local neighbourhood. Ultimately, it helps everybody's learning and brings communities together.

Having worked in a wide variety of schools, both selective and non-selective, I can understand where these headteachers are coming from: their schools will improve their results under the Tories' plans because it will be much easier to gerrymander the admissions process. But it won't be fair to society as a whole: the divisions between rich and poor will be greatly exacerbated. What's so disturbing though is that none of the political parties are willing to address this issue. As organisations such as Case and Comprehensive Future have noted, what we need is a much fairer education system where all children are given an equal chance, where selection is abolished, and where schools are made accountable to their local communities and where teachers are supported in all schools, not just a privileged few.

If Britain is indeed "broken", as David Cameron claims it is, it will be well and truly smashed up by these insane education plans. With no local authorities to plan for crucial things like rising and falling birthrates, for making provision for special educational needs pupils, for English as an additional language learners, for our most disadvantaged children, chaos will surely follow. Even more iniquitously, with maintained schools being starved of cash in order to fund "free" schools and fairer admissions policies being thrown out of the window, we will see a free-for-all which will fracture our communities and corrupt school standards even further.